The White House said the president had a duty to not leave servicemembers behind.
Key Dems hailed the plan while some Republicans called for even more flexibility.
The Senate is matching the House's overall defense spending.
The House GOP budget for fiscal 2016 provides $613 in total defense spending.
GOP senators say Obama's war plan leaves the rebels open to Assad's attacks.
Lawmakers remain skeptical of Obama's proposed ISIS war measure.
Senate Dems who backed the bill had vowed to vote no.
"It's a very bad deal. We're better off without it," he told lawmakers.
The top Dem on House Armed Services said he was "skeptical" the measure would pass.
The White House request has faced criticism from the GOP and Dems.
Ashton Carter, 60, will be the 25th secretary of Defense and Obama's fourth.
It is unclear if the language will pass muster with Dems.
The charges renewed debate over the Taliban swap to secure his release.
Officials will keep most of the 10,000 troops in Afghanistan through 2015.
Defense hawks are giving GOP leaders breathing room to pass their blueprint.
The Armed Services chairmen want to lift spending caps on defense.
Officials on Wednesday struggled to make the case for Obama's war measure.
Critics said the letter from 47 Republicans undermined the president's policy.
Clinton used personal email exclusively while at the State Department.
The Israeli leader will deliver his controversial address at 11 a.m. Tuesday.
The head of anti-ISIS coalition wouldn't define the key language.
Lawmakers from both parties have panned Obama's request for authorization of force.
Obama's war powers request was met with skepticism from both parties.
Pressure is building on Obama to bolster aid to Kiev.